A sequence estimator, as a form of equalizer, processes a sequence of information symbols that has been received over a dispersive channel with inter-symbol interference. A Maximum Likelihood Sequence Estimator (MLSE), for example, operates on a trellis of possible sequences to determine the most likely path associated with the received sequence. The computational complexity of an MLSE, however, becomes particularly burdensome with an increasing number of possible paths represented by the sequence (which is a function of the sequence length, as well as the number of possible symbol values).
To reduce computational complexity, some sequence estimators eliminate certain paths from sequence estimation. In particular, Generalized MLSE Arbitration (GMA) greatly reduces the number of possible paths considered by an MLSE through use of a two-pass demodulation process. The first pass identifies a reduced set of possible values for each symbol in the sequence, such as by detecting the most likely possible values out of all possible values defined by the modulation constellation. The state space for each symbol in the second pass is then constrained to the reduced set identified for that symbol in the first pass. Accordingly, an MLSE in the second pass considers fewer paths of possible symbol sequences in detecting the received sequence. For a more detailed discussion of GMA, see U.S. patent application Ser. No. 12/035,932, which is co-owned with the instant application.
With a reduced state space, however, these sequence estimators can produce insufficient reliability, or soft, information about the bits detected. In fact, some of the states used to generate this soft information (e.g., those corresponding to a bit value other than that detected) may be missing from the trellis entirely. Thus, although eliminating paths during sequence estimation reduces computational complexity, such compromises the additional error correcting performance obtained from soft information.